Joint work with Thomas Duquesne on Growth of Levy forests

It is well-known that the only space-time scaling limits of Galton-Watson processes are continuous-state branching processes. Their genealogical structure is most explicitly expressed by discrete trees and R-trees, respectively. Weak limit theorems have been recently established for some of these random trees. We study here a Markovian forest growth procedure that allows to construct the genealogical forest of any continuous-state branching process with immigration as an a.s. limit of Galton-Watson forests with edge lengths. Furthermore, we are naturally led to continuous forests with edge lengths. Another strength of our method is that it yields results in the general supercritical case that was excluded in most of the previous literature.